Integrating Other Functions (Cambridge (CIE) A Level Maths: Pure 3): Revision Note

Integrating other functions

Is integration the reverse of differentiation?

• Yes, but remember “+c”, the constant of integration …

  • … unless finding a definite integral

• Recognising common results helps to make integration easier

  (See Differentiating Other Functions)

• You are given all the standard integrals in the formula booklet

How do I integrate e^x and e^kx?

• The gradient of e^kx is ke^kx

  • ie y = e^kx, dy/dx = ke^kx

• The reverse applies when integrating

• This is an example of reverse chain rule

How do I integrating 1/x?

• Remember 1/x = x^-1

  • The method for integrating powers does not apply if the power is -1

How do I integrating sin x and cos x?

• Note the minus in the integral of sin x

How do I integrate tan x?

• The integral of tan x is ln|sec x| + c

How do I integrate and ?

• Recall that 

• Then  and